benchmarkfcns.ackleyn4

benchmarkfcns.ackleyn4(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of Ackley N. 4 benchmark function. SCORES = ackley4(X) computes the value of the Ackley function at point X. ackley4 accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1 in which each row contains the function value for each row of X. Properties:

  • Global minimum: -4.590101 (approximately)

  • Location of global minimum: (1.47925, -1.47925)

  • Number of dimensions: 2

  • Recommended domain: x_1, x_2 ∈ [-35, 35]

  • Number of local minima: Numerous (Highly oscillatory)

  • Number of global minima: 2 (typically symmetric across the origin)

  • Convexity: Non-convex

  • Separability: Non-separable

  • Modality: Multimodal

  • Symmetry: Symmetric (with respect to the origin/axes due to the absolute values)

  • Differentiable: No

For more information, please visit: benchmarkfcns.info/doc/ackleyn4fcn

Mathematical Definition

Visualization

ackleyn4 landscape